Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields,and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Ferroelectric domain walls constitute a completely new class of sheet-like functional material. Moreover, since domain walls are generally writable, erasable and mobile, they could be useful in functionally agile devices: for example, creating and moving conducting walls could make or break electrical connections in new forms of reconfigurable nanocircuitry. However, significant challenges exist: site-specific injection and annihilation of planar walls, which show robust conductivity, has not been easy to achieve. Here, we report the observation, mechanical writing and controlled movement of charged conducting domain walls in the improper-ferroelectric Cu3B7O13Cl. Walls are straight, tens of microns long and exist as a consequence of elastic compatibility conditions between specific domain pairs. We show that site-specific injection of conducting walls of up to hundreds of microns in length can be achieved through locally applied point-stress and, once created, that they can be moved and repositioned using applied electric fields.

Enhanced conductivity at specific domain walls in ferroelectrics is now an established phenomenon. Surprisingly, however, little is known about the most fundamental aspects of conduction. Carrier types, densities and mobilities have not been determined and transport mechanisms are still a matter of guesswork. Here we demonstrate that intermittent-contact atomic force microscopy (AFM) can detect the Hall effect in conducting domain walls. Studying YbMnO3 single crystals, we have confirmed that p-type conduction occurs in tail-to-tail charged domain walls. By calibration of the AFM signal, an upper estimate of ∼1 × 1016 cm−3 is calculated for the mobile carrier density in the wall, around four orders of magnitude below that required for complete screening of the polar discontinuity. A carrier mobility of∼50 cm2V−1s−1 is calculated, about an order of magnitude below equivalent carrier mobilities in p-type silicon, but sufficiently high to preclude carrier-lattice coupling associated with small polarons.

Ferroelectric domain wall injection has been demonstrated by engineering of the local electric field, using focused ion beam milled defects in thin single crystal lamellae of KTiOPO4 (KTP). The electric field distribution (top) displays localized field hot-spots, which correlate with nucleation events (bottom). Designed local field variations can also dictate subsequent domain wall mobility, demonstrating a new paradigm in ferroelectric domain wall control.

Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.